Step-by-step explanation:
√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))
Square and take the square root.
√[√((1 + sin x) / (1 − sin x)) + √((1 − sin x) / (1 + sin x))]²
√[(1 + sin x) / (1 − sin x) + 2 + (1 − sin x) / (1 + sin x)]
Add the fractions using least common denominator.
√[((1 + sin x)² + (1 − sin x)²) / (1 − sin²x) + 2]
√[(1 + 2 sin x + sin²x + 1 − 2 sin x + sin²x) / (1 − sin²x) + 2]
√[(2 + 2 sin²x) / (1 − sin²x) + 2]
Use Pythagorean identity:
√[(2 + 2 sin²x) / (cos²x) + 2]
√[2 sec²x + 2 tan²x + 2]
√[2 sec²x + 2 (tan²x + 1)]
Use Pythagorean identity:
√[2 sec²x + 2 sec²x]
√[4 sec²x]
±2 sec x
If x is in the second quadrant, then sec x < 0.
-2 sec x
Answer:
Step-by-step explanation:
x^2+20=2x move 2x to the left
x^2-2x+20=0
Quadratic formula =
x=1± i√19
Upper Tolerance
Remark
The 11/16 is the only thing that will be affected. The three won't go up or down when we add 1/64 so we should just work with the 11/16. We need only add 11/16 and 1/64 together to see what the upper range is. Later on we can add 3 into the mix.
Solution
<u>Upper Limit</u>

Now change the 11/16 into 64. Multiply numerator and denominator or 11/16 by 4

Which results in

With a final result for the fractions of 45/64
So the upper tolerance = 3 45/64
<u>Lower Tolerance</u>
Just follow the same steps as you did for the upper tolerance except you subtract 1/64 like this.

Your answer should be 3 and 43/64